Related papers: Geometrization of Classical Wave Fields
Given a computer model of a physical object, it is often quite difficult to visualize and quantify any global effects on the shape representation caused by local uncertainty and local errors in the data. This problem is further amplified…
We introduce topological gauge fields as nontrivial field configurations enforced by topological currents. These fields crucially determine the form of statistical gauge fields that couple to matter and transmute their statistics. We…
Topological defects in solids, usually described by complicated boundary conditions in elastic theory, may be described more simply as sources of a gravity- like deformation field in the geometric approach of Katanaev and Volovich. This…
The space-time curvature carried by electromagnetic fields is discovered and a new unification of geometry and electromagnetism is found. Curvature is invariant under charge reversal symmetry. Electromagnetic field equations are examined…
A new approach is proposed for an electromagnetic field geometrisation. We show that interacting Maxwell and Dirac fields can be considered as a single connected space-time 4-manifold. The Dirac spinors appear wihtin such approach as basic…
Liquid crystals generally support orientational singularities of the director field known as topological defects. These latter modifiy transport properties in their vicinity as if the geometry was non-Euclidean. We present a state of the…
Information geometry is concerned with the application of differential geometry concepts in the study of the parametric spaces of statistical models. When the random variables are independent and identically distributed, the underlying…
Quantum experiments detect particles, but they reveal information about wave properties. No matter how quanta are detected, they always express the local net state of the corresponding wave-function. The mechanism behind this process is…
A deformation of the wave equation on a two-dimensional black hole is considered as a toy-model for possible gravitational or stringy nonlocal effects. The deformed wave-equation allows for an initial-value problem despite being nonlocal.…
In this article, the ray tracing method is studied beyond the classical geometrical theory. The trajectories are here regarded as geodesics in a Riemannian manifold, whose metric and topological properties are those induced by the…
A process-theoretic approach to electrodynamics based on persistent Kac-type stochastic processes is developed. Finite-velocity stochastic propagation is taken as primary, while relativistic wave equations arise as emergent descriptions…
In non-relativistic physics, the concepts of geometry and topology are usually applied to characterize spatial structures or structures in momentum space. We introduce the concept of temporal geometry, which encompasses the geometric and…
Within the framework of classical field theory, the connection between the Dirac field as the field of matter and the spacetime metric is discussed. Polarization structure of the Dirac field is shown to be rich enough to determine the…
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a…
An exact analogy of electromagnetic fields and particles can be found in continuum mechanics of a turbulent perfect fluid with voids. Deviations of the turbulence from a homogeneous isotropic state correspond to electromagnetic fields: with…
We present a method developed to deal with electromagnetic wave propagation inside a material medium that reacts, in general, non-linearly to the field strength. We work in the context of Maxwell' s theory in the low frequency limit and…
A new approach to the geometrization of the electron theory is proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
A derivation of the properties of pulsed radiative imaging systems is presented with examples drawn from conventional, synthetic aperture, and interferometric radar. A geometric construction of the space and time components of a radar…
Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a…